Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Approximate and pseudo-amenability of various classes of Banach algebras
AU - Choi, Yemon
AU - Ghahramani, Fereidoun
AU - Zhang, Yong
PY - 2009/5/15
Y1 - 2009/5/15
N2 - We continue the investigation of notions of approximate amenability that were introduced in work of the second and third authors together with R.J. Loy. It is shown that every boundedly approximately contractible Banach algebra has a bounded approximate identity, and that the Fourier algebra of the free group on two generators is not operator approximately amenable. Further examples are obtained of ℓ1-semigroup algebras which are approximately amenable but not amenable; using these, we show that bounded approximate contractibility need not imply sequential approximate amenability. Results are also given for Segal algebras on locally compact groups, and algebras of p-pseudo-functions on discrete groups.
AB - We continue the investigation of notions of approximate amenability that were introduced in work of the second and third authors together with R.J. Loy. It is shown that every boundedly approximately contractible Banach algebra has a bounded approximate identity, and that the Fourier algebra of the free group on two generators is not operator approximately amenable. Further examples are obtained of ℓ1-semigroup algebras which are approximately amenable but not amenable; using these, we show that bounded approximate contractibility need not imply sequential approximate amenability. Results are also given for Segal algebras on locally compact groups, and algebras of p-pseudo-functions on discrete groups.
KW - Amenable Banach algebra
KW - Amenable group
KW - Approximately amenable Banach algebra
KW - Approximate diagonal
KW - Approximate identity
KW - Fourier algebra
KW - Segal algebra
KW - Semigroup algebra
KW - Reduced C∗-algebra
U2 - 10.1016/j.jfa.2009.02.012
DO - 10.1016/j.jfa.2009.02.012
M3 - Journal article
VL - 256
SP - 3158
EP - 3191
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 10
ER -